LMFDB - Embedded newform 700.2.c.b.699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(699,700)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("700.699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			699.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	700.699
Dual form			700.2.c.b.699.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 + 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 + 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} -0.267949i q^{11} +(1.73205 - 3.00000i) q^{12} +0.464102 q^{13} +(3.36603 - 1.63397i) q^{14} +(2.00000 + 3.46410i) q^{16} -6.46410 q^{17} -6.00000 q^{19} +(3.00000 + 3.46410i) q^{21} +(-0.0980762 + 0.366025i) q^{22} +1.46410 q^{23} +(-3.46410 + 3.46410i) q^{24} +(-0.633975 - 0.169873i) q^{26} -5.19615i q^{27} +(-5.19615 + 1.00000i) q^{28} -7.92820 q^{29} -6.00000 q^{31} +(-1.46410 - 5.46410i) q^{32} -0.464102 q^{33} +(8.83013 + 2.36603i) q^{34} +9.46410i q^{37} +(8.19615 + 2.19615i) q^{38} -0.803848i q^{39} -3.46410i q^{41} +(-2.83013 - 5.83013i) q^{42} +2.00000 q^{43} +(0.267949 - 0.464102i) q^{44} +(-2.00000 - 0.535898i) q^{46} -1.73205i q^{47} +(6.00000 - 3.46410i) q^{48} +(1.00000 - 6.92820i) q^{49} +11.1962i q^{51} +(0.803848 + 0.464102i) q^{52} +2.00000i q^{53} +(-1.90192 + 7.09808i) q^{54} +(7.46410 + 0.535898i) q^{56} +10.3923i q^{57} +(10.8301 + 2.90192i) q^{58} +3.46410 q^{59} +9.46410i q^{61} +(8.19615 + 2.19615i) q^{62} +8.00000i q^{64} +(0.633975 + 0.169873i) q^{66} +3.46410 q^{67} +(-11.1962 - 6.46410i) q^{68} -2.53590i q^{69} -7.46410i q^{71} -12.9282 q^{73} +(3.46410 - 12.9282i) q^{74} +(-10.3923 - 6.00000i) q^{76} +(0.464102 + 0.535898i) q^{77} +(-0.294229 + 1.09808i) q^{78} +14.6603i q^{79} -9.00000 q^{81} +(-1.26795 + 4.73205i) q^{82} +15.4641i q^{83} +(1.73205 + 9.00000i) q^{84} +(-2.73205 - 0.732051i) q^{86} +13.7321i q^{87} +(-0.535898 + 0.535898i) q^{88} -2.53590i q^{89} +(-0.928203 + 0.803848i) q^{91} +(2.53590 + 1.46410i) q^{92} +10.3923i q^{93} +(-0.633975 + 2.36603i) q^{94} +(-9.46410 + 2.53590i) q^{96} -13.3923 q^{97} +(-3.90192 + 9.09808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{6} - 8 q^{7} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^6 - 8 * q^7 - 8 * q^8	$ 4 q - 2 q^{2} - 6 q^{6} - 8 q^{7} - 8 q^{8} - 12 q^{13} + 10 q^{14} + 8 q^{16} - 12 q^{17} - 24 q^{19} + 12 q^{21} + 10 q^{22} - 8 q^{23} - 6 q^{26} - 4 q^{29} - 24 q^{31} + 8 q^{32} + 12 q^{33} + 18 q^{34} + 12 q^{38} + 6 q^{42} + 8 q^{43} + 8 q^{44} - 8 q^{46} + 24 q^{48} + 4 q^{49} + 24 q^{52} - 18 q^{54} + 16 q^{56} + 26 q^{58} + 12 q^{62} + 6 q^{66} - 24 q^{68} - 24 q^{73} - 12 q^{77} + 30 q^{78} - 36 q^{81} - 12 q^{82} - 4 q^{86} - 16 q^{88} + 24 q^{91} + 24 q^{92} - 6 q^{94} - 24 q^{96} - 12 q^{97} - 26 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^6 - 8 * q^7 - 8 * q^8 - 12 * q^13 + 10 * q^14 + 8 * q^16 - 12 * q^17 - 24 * q^19 + 12 * q^21 + 10 * q^22 - 8 * q^23 - 6 * q^26 - 4 * q^29 - 24 * q^31 + 8 * q^32 + 12 * q^33 + 18 * q^34 + 12 * q^38 + 6 * q^42 + 8 * q^43 + 8 * q^44 - 8 * q^46 + 24 * q^48 + 4 * q^49 + 24 * q^52 - 18 * q^54 + 16 * q^56 + 26 * q^58 + 12 * q^62 + 6 * q^66 - 24 * q^68 - 24 * q^73 - 12 * q^77 + 30 * q^78 - 36 * q^81 - 12 * q^82 - 4 * q^86 - 16 * q^88 + 24 * q^91 + 24 * q^92 - 6 * q^94 - 24 * q^96 - 12 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$		−	1.73205i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$		−	1.73205i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$		0			0
$5$		0			0
$6$	−0.633975	+	2.36603i	−0.258819	+	0.965926i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		0			0
$10$		0			0
$11$		−	0.267949i		−	0.0807897i	−0.999184	−	0.0403949i	$-0.987138\pi$
$11$		−	0.267949i		−	0.0807897i	0.999184	−	0.0403949i	$-0.0128616\pi$
$12$	1.73205	−	3.00000i	0.500000	−	0.866025i
$13$	0.464102			0.128719			0.0643593	−	0.997927i	$-0.479500\pi$
$13$	0.464102			0.128719			0.0643593	+	0.997927i	$0.479500\pi$
$14$	3.36603	−	1.63397i	0.899608	−	0.436698i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−6.46410			−1.56777			−0.783887	−	0.620903i	$-0.786766\pi$
$17$	−6.46410			−1.56777			−0.783887	+	0.620903i	$0.786766\pi$
$18$		0			0
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$		0			0
$21$	3.00000	+	3.46410i	0.654654	+	0.755929i
$22$	−0.0980762	+	0.366025i	−0.0209099	+	0.0780369i
$23$	1.46410			0.305286			0.152643	−	0.988281i	$-0.451221\pi$
$23$	1.46410			0.305286			0.152643	+	0.988281i	$0.451221\pi$
$24$	−3.46410	+	3.46410i	−0.707107	+	0.707107i
$25$		0			0
$26$	−0.633975	−	0.169873i	−0.124333	−	0.0333148i
$27$		−	5.19615i		−	1.00000i
$28$	−5.19615	+	1.00000i	−0.981981	+	0.188982i
$29$	−7.92820			−1.47223			−0.736115	−	0.676856i	$-0.763342\pi$
$29$	−7.92820			−1.47223			−0.736115	+	0.676856i	$0.763342\pi$
$30$		0			0
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$	−0.464102			−0.0807897
$34$	8.83013	+	2.36603i	1.51435	+	0.405770i
$35$		0			0
$36$		0			0
$37$			9.46410i			1.55589i	0.628333	+	0.777944i	$0.283737\pi$
$37$			9.46410i			1.55589i	−0.628333	+	0.777944i	$0.716263\pi$
$38$	8.19615	+	2.19615i	1.32959	+	0.356263i
$39$		−	0.803848i		−	0.128719i
$40$		0			0
$41$		−	3.46410i		−	0.541002i	−0.962720	−	0.270501i	$-0.912811\pi$
$41$		−	3.46410i		−	0.541002i	0.962720	−	0.270501i	$-0.0871893\pi$
$42$	−2.83013	−	5.83013i	−0.436698	−	0.899608i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	0.267949	−	0.464102i	0.0403949	−	0.0699660i
$45$		0			0
$46$	−2.00000	−	0.535898i	−0.294884	−	0.0790139i
$47$		−	1.73205i		−	0.252646i	−0.991989	−	0.126323i	$-0.959682\pi$
$47$		−	1.73205i		−	0.252646i	0.991989	−	0.126323i	$-0.0403175\pi$
$48$	6.00000	−	3.46410i	0.866025	−	0.500000i
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$			11.1962i			1.56777i
$52$	0.803848	+	0.464102i	0.111474	+	0.0643593i
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	−1.90192	+	7.09808i	−0.258819	+	0.965926i
$55$		0			0
$56$	7.46410	+	0.535898i	0.997433	+	0.0716124i
$57$			10.3923i			1.37649i
$58$	10.8301	+	2.90192i	1.42207	+	0.381041i
$59$	3.46410			0.450988			0.225494	−	0.974245i	$-0.427600\pi$
$59$	3.46410			0.450988			0.225494	+	0.974245i	$0.427600\pi$
$60$		0			0
$61$			9.46410i			1.21175i	0.795558	+	0.605877i	$0.207178\pi$
$61$			9.46410i			1.21175i	−0.795558	+	0.605877i	$0.792822\pi$
$62$	8.19615	+	2.19615i	1.04091	+	0.278912i
$63$		0			0
$64$			8.00000i			1.00000i
$65$		0			0
$66$	0.633975	+	0.169873i	0.0780369	+	0.0209099i
$67$	3.46410			0.423207			0.211604	−	0.977356i	$-0.432131\pi$
$67$	3.46410			0.423207			0.211604	+	0.977356i	$0.432131\pi$
$68$	−11.1962	−	6.46410i	−1.35773	−	0.783887i
$69$		−	2.53590i		−	0.305286i
$70$		0			0
$71$		−	7.46410i		−	0.885826i	−0.896565	−	0.442913i	$-0.853945\pi$
$71$		−	7.46410i		−	0.885826i	0.896565	−	0.442913i	$-0.146055\pi$
$72$		0			0
$73$	−12.9282			−1.51313			−0.756566	−	0.653917i	$-0.773124\pi$
$73$	−12.9282			−1.51313			−0.756566	+	0.653917i	$0.773124\pi$
$74$	3.46410	−	12.9282i	0.402694	−	1.50287i
$75$		0			0
$76$	−10.3923	−	6.00000i	−1.19208	−	0.688247i
$77$	0.464102	+	0.535898i	0.0528893	+	0.0610713i
$78$	−0.294229	+	1.09808i	−0.0333148	+	0.124333i
$79$			14.6603i			1.64941i	0.565565	+	0.824704i	$0.308658\pi$
$79$			14.6603i			1.64941i	−0.565565	+	0.824704i	$0.691342\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$	−1.26795	+	4.73205i	−0.140022	+	0.522568i
$83$			15.4641i			1.69741i	0.528870	+	0.848703i	$0.322616\pi$
$83$			15.4641i			1.69741i	−0.528870	+	0.848703i	$0.677384\pi$
$84$	1.73205	+	9.00000i	0.188982	+	0.981981i
$85$		0			0
$86$	−2.73205	−	0.732051i	−0.294605	−	0.0789391i
$87$			13.7321i			1.47223i
$88$	−0.535898	+	0.535898i	−0.0571270	+	0.0571270i
$89$		−	2.53590i		−	0.268805i	−0.990927	−	0.134402i	$-0.957089\pi$
$89$		−	2.53590i		−	0.268805i	0.990927	−	0.134402i	$-0.0429115\pi$
$90$		0			0
$91$	−0.928203	+	0.803848i	−0.0973021	+	0.0842661i
$92$	2.53590	+	1.46410i	0.264386	+	0.152643i
$93$			10.3923i			1.07763i
$94$	−0.633975	+	2.36603i	−0.0653895	+	0.244037i
$95$		0			0
$96$	−9.46410	+	2.53590i	−0.965926	+	0.258819i
$97$	−13.3923			−1.35978			−0.679891	−	0.733313i	$-0.737973\pi$
$97$	−13.3923			−1.35978			−0.679891	+	0.733313i	$0.737973\pi$
$98$	−3.90192	+	9.09808i	−0.394154	+	0.919044i
$99$		0			0
$100$		0			0
$101$		−	15.4641i		−	1.53874i	−0.638806	−	0.769368i	$-0.720571\pi$
$101$		−	15.4641i		−	1.53874i	0.638806	−	0.769368i	$-0.279429\pi$
$102$	4.09808	−	15.2942i	0.405770	−	1.51435i
$103$		−	6.80385i		−	0.670403i	−0.942146	−	0.335202i	$-0.891196\pi$
$103$		−	6.80385i		−	0.670403i	0.942146	−	0.335202i	$-0.108804\pi$
$104$	−0.928203	−	0.928203i	−0.0910178	−	0.0910178i
$105$		0			0
$106$	0.732051	−	2.73205i	0.0711031	−	0.265360i
$107$	2.39230			0.231273			0.115636	−	0.993292i	$-0.463109\pi$
$107$	2.39230			0.231273			0.115636	+	0.993292i	$0.463109\pi$
$108$	5.19615	−	9.00000i	0.500000	−	0.866025i
$109$	−2.07180			−0.198442			−0.0992211	−	0.995065i	$-0.531635\pi$
$109$	−2.07180			−0.198442			−0.0992211	+	0.995065i	$0.531635\pi$
$110$		0			0
$111$	16.3923			1.55589
$112$	−10.0000	−	3.46410i	−0.944911	−	0.327327i
$113$			5.46410i			0.514019i	0.966409	+	0.257010i	$0.0827372\pi$
$113$			5.46410i			0.514019i	−0.966409	+	0.257010i	$0.917263\pi$
$114$	3.80385	−	14.1962i	0.356263	−	1.32959i
$115$		0			0
$116$	−13.7321	−	7.92820i	−1.27499	−	0.736115i
$117$		0			0
$118$	−4.73205	−	1.26795i	−0.435621	−	0.116724i
$119$	12.9282	−	11.1962i	1.18513	−	1.02635i
$120$		0			0
$121$	10.9282			0.993473
$122$	3.46410	−	12.9282i	0.313625	−	1.17046i
$123$	−6.00000			−0.541002
$124$	−10.3923	−	6.00000i	−0.933257	−	0.538816i
$125$		0			0
$126$		0			0
$127$	15.4641			1.37222			0.686109	−	0.727499i	$-0.259317\pi$
$127$	15.4641			1.37222			0.686109	+	0.727499i	$0.259317\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$		−	3.46410i		−	0.304997i
$130$		0			0
$131$	2.53590			0.221562			0.110781	−	0.993845i	$-0.464665\pi$
$131$	2.53590			0.221562			0.110781	+	0.993845i	$0.464665\pi$
$132$	−0.803848	−	0.464102i	−0.0699660	−	0.0403949i
$133$	12.0000	−	10.3923i	1.04053	−	0.901127i
$134$	−4.73205	−	1.26795i	−0.408787	−	0.109534i
$135$		0			0
$136$	12.9282	+	12.9282i	1.10858	+	1.10858i
$137$		−	20.3923i		−	1.74223i	−0.491077	−	0.871116i	$-0.663397\pi$
$137$		−	20.3923i		−	1.74223i	0.491077	−	0.871116i	$-0.336603\pi$
$138$	−0.928203	+	3.46410i	−0.0790139	+	0.294884i
$139$	−6.92820			−0.587643			−0.293821	−	0.955860i	$-0.594927\pi$
$139$	−6.92820			−0.587643			−0.293821	+	0.955860i	$0.594927\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	−2.73205	+	10.1962i	−0.229269	+	0.855642i
$143$		−	0.124356i		−	0.0103991i
$144$		0			0
$145$		0			0
$146$	17.6603	+	4.73205i	1.46157	+	0.391627i
$147$	−12.0000	−	1.73205i	−0.989743	−	0.142857i
$148$	−9.46410	+	16.3923i	−0.777944	+	1.34744i
$149$	−3.07180			−0.251651			−0.125826	−	0.992052i	$-0.540158\pi$
$149$	−3.07180			−0.251651			−0.125826	+	0.992052i	$0.540158\pi$
$150$		0			0
$151$		−	15.1962i		−	1.23665i	−0.785924	−	0.618323i	$-0.787812\pi$
$151$		−	15.1962i		−	1.23665i	0.785924	−	0.618323i	$-0.212188\pi$
$152$	12.0000	+	12.0000i	0.973329	+	0.973329i
$153$		0			0
$154$	−0.437822	−	0.901924i	−0.0352807	−	0.0726791i
$155$		0			0
$156$	0.803848	−	1.39230i	0.0643593	−	0.111474i
$157$	7.85641			0.627009			0.313505	−	0.949587i	$-0.398497\pi$
$157$	7.85641			0.627009			0.313505	+	0.949587i	$0.398497\pi$
$158$	5.36603	−	20.0263i	0.426898	−	1.59321i
$159$	3.46410			0.274721
$160$		0			0
$161$	−2.92820	+	2.53590i	−0.230775	+	0.199857i
$162$	12.2942	+	3.29423i	0.965926	+	0.258819i
$163$	−20.7846			−1.62798			−0.813988	−	0.580881i	$-0.802708\pi$
$163$	−20.7846			−1.62798			−0.813988	+	0.580881i	$0.802708\pi$
$164$	3.46410	−	6.00000i	0.270501	−	0.468521i
$165$		0			0
$166$	5.66025	−	21.1244i	0.439321	−	1.63957i
$167$			5.19615i			0.402090i	0.979582	+	0.201045i	$0.0644338\pi$
$167$			5.19615i			0.402090i	−0.979582	+	0.201045i	$0.935566\pi$
$168$	0.928203	−	12.9282i	0.0716124	−	0.997433i
$169$	−12.7846			−0.983432
$170$		0			0
$171$		0			0
$172$	3.46410	+	2.00000i	0.264135	+	0.152499i
$173$	14.3205			1.08877			0.544384	−	0.838836i	$-0.316763\pi$
$173$	14.3205			1.08877			0.544384	+	0.838836i	$0.316763\pi$
$174$	5.02628	−	18.7583i	0.381041	−	1.42207i
$175$		0			0
$176$	0.928203	−	0.535898i	0.0699660	−	0.0403949i
$177$		−	6.00000i		−	0.450988i
$178$	−0.928203	+	3.46410i	−0.0695718	+	0.259645i
$179$		−	6.39230i		−	0.477783i	−0.971046	−	0.238892i	$-0.923216\pi$
$179$		−	6.39230i		−	0.477783i	0.971046	−	0.238892i	$-0.0767841\pi$
$180$		0			0
$181$		−	0.928203i		−	0.0689928i	−0.999405	−	0.0344964i	$-0.989017\pi$
$181$		−	0.928203i		−	0.0689928i	0.999405	−	0.0344964i	$-0.0109827\pi$
$182$	1.56218	−	0.758330i	0.115796	−	0.0562112i
$183$	16.3923			1.21175
$184$	−2.92820	−	2.92820i	−0.215870	−	0.215870i
$185$		0			0
$186$	3.80385	−	14.1962i	0.278912	−	1.04091i
$187$			1.73205i			0.126660i
$188$	1.73205	−	3.00000i	0.126323	−	0.218797i
$189$	9.00000	+	10.3923i	0.654654	+	0.755929i
$190$		0			0
$191$		−	7.19615i		−	0.520695i	−0.965515	−	0.260348i	$-0.916163\pi$
$191$		−	7.19615i		−	0.520695i	0.965515	−	0.260348i	$-0.0838372\pi$
$192$	13.8564			1.00000
$193$		−	9.46410i		−	0.681241i	−0.940201	−	0.340620i	$-0.889363\pi$
$193$		−	9.46410i		−	0.681241i	0.940201	−	0.340620i	$-0.110637\pi$
$194$	18.2942	+	4.90192i	1.31345	+	0.351938i
$195$		0			0
$196$	8.66025	−	11.0000i	0.618590	−	0.785714i
$197$			13.3205i			0.949047i	0.880243	+	0.474523i	$0.157380\pi$
$197$			13.3205i			0.949047i	−0.880243	+	0.474523i	$0.842620\pi$
$198$		0			0
$199$	−3.46410			−0.245564			−0.122782	−	0.992434i	$-0.539182\pi$
$199$	−3.46410			−0.245564			−0.122782	+	0.992434i	$0.539182\pi$
$200$		0			0
$201$		−	6.00000i		−	0.423207i
$202$	−5.66025	+	21.1244i	−0.398254	+	1.48630i
$203$	15.8564	−	13.7321i	1.11290	−	0.963801i
$204$	−11.1962	+	19.3923i	−0.783887	+	1.35773i
$205$		0			0
$206$	−2.49038	+	9.29423i	−0.173513	+	0.647560i
$207$		0			0
$208$	0.928203	+	1.60770i	0.0643593	+	0.111474i
$209$			1.60770i			0.111207i
$210$		0			0
$211$		−	3.19615i		−	0.220032i	−0.993930	−	0.110016i	$-0.964910\pi$
$211$		−	3.19615i		−	0.220032i	0.993930	−	0.110016i	$-0.0350902\pi$
$212$	−2.00000	+	3.46410i	−0.137361	+	0.237915i
$213$	−12.9282			−0.885826
$214$	−3.26795	−	0.875644i	−0.223392	−	0.0598578i
$215$		0			0
$216$	−10.3923	+	10.3923i	−0.707107	+	0.707107i
$217$	12.0000	−	10.3923i	0.814613	−	0.705476i
$218$	2.83013	+	0.758330i	0.191680	+	0.0513606i
$219$			22.3923i			1.51313i
$220$		0			0
$221$	−3.00000			−0.201802
$222$	−22.3923	−	6.00000i	−1.50287	−	0.402694i
$223$		−	13.7321i		−	0.919566i	−0.888031	−	0.459783i	$-0.847927\pi$
$223$		−	13.7321i		−	0.919566i	0.888031	−	0.459783i	$-0.152073\pi$
$224$	12.3923	+	8.39230i	0.827996	+	0.560734i
$225$		0			0
$226$	2.00000	−	7.46410i	0.133038	−	0.496505i
$227$		−	20.6603i		−	1.37127i	−0.727946	−	0.685635i	$-0.759525\pi$
$227$		−	20.6603i		−	1.37127i	0.727946	−	0.685635i	$-0.240475\pi$
$228$	−10.3923	+	18.0000i	−0.688247	+	1.19208i
$229$			8.53590i			0.564068i	0.959404	+	0.282034i	$0.0910091\pi$
$229$			8.53590i			0.564068i	−0.959404	+	0.282034i	$0.908991\pi$
$230$		0			0
$231$	0.928203	−	0.803848i	0.0610713	−	0.0528893i
$232$	15.8564	+	15.8564i	1.04102	+	1.04102i
$233$		−	9.07180i		−	0.594313i	−0.954829	−	0.297157i	$-0.903962\pi$
$233$		−	9.07180i		−	0.594313i	0.954829	−	0.297157i	$-0.0960383\pi$
$234$		0			0
$235$		0			0
$236$	6.00000	+	3.46410i	0.390567	+	0.225494i
$237$	25.3923			1.64941
$238$	−21.7583	+	10.5622i	−1.41038	+	0.684644i
$239$		−	23.9808i		−	1.55119i	−0.631233	−	0.775593i	$-0.717451\pi$
$239$		−	23.9808i		−	1.55119i	0.631233	−	0.775593i	$-0.282549\pi$
$240$		0			0
$241$			16.3923i			1.05592i	0.849269	+	0.527961i	$0.177043\pi$
$241$			16.3923i			1.05592i	−0.849269	+	0.527961i	$0.822957\pi$
$242$	−14.9282	−	4.00000i	−0.959621	−	0.257130i
$243$		0			0
$244$	−9.46410	+	16.3923i	−0.605877	+	1.04941i
$245$		0			0
$246$	8.19615	+	2.19615i	0.522568	+	0.140022i
$247$	−2.78461			−0.177180
$248$	12.0000	+	12.0000i	0.762001	+	0.762001i
$249$	26.7846			1.69741
$250$		0			0
$251$	−25.8564			−1.63204			−0.816021	−	0.578022i	$-0.803825\pi$
$251$	−25.8564			−1.63204			−0.816021	+	0.578022i	$0.803825\pi$
$252$		0			0
$253$		−	0.392305i		−	0.0246640i
$254$	−21.1244	−	5.66025i	−1.32546	−	0.355156i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$	−1.26795	+	4.73205i	−0.0789391	+	0.294605i
$259$	−16.3923	−	18.9282i	−1.01857	−	1.17614i
$260$		0			0
$261$		0			0
$262$	−3.46410	−	0.928203i	−0.214013	−	0.0573446i
$263$	−11.4641			−0.706907			−0.353453	−	0.935452i	$-0.614993\pi$
$263$	−11.4641			−0.706907			−0.353453	+	0.935452i	$0.614993\pi$
$264$	0.928203	+	0.928203i	0.0571270	+	0.0571270i
$265$		0			0
$266$	−20.1962	+	9.80385i	−1.23831	+	0.601112i
$267$	−4.39230			−0.268805
$268$	6.00000	+	3.46410i	0.366508	+	0.211604i
$269$			12.0000i			0.731653i	0.930683	+	0.365826i	$0.119214\pi$
$269$			12.0000i			0.731653i	−0.930683	+	0.365826i	$0.880786\pi$
$270$		0			0
$271$	9.46410			0.574903			0.287452	−	0.957795i	$-0.407192\pi$
$271$	9.46410			0.574903			0.287452	+	0.957795i	$0.407192\pi$
$272$	−12.9282	−	22.3923i	−0.783887	−	1.35773i
$273$	1.39230	+	1.60770i	0.0842661	+	0.0973021i
$274$	−7.46410	+	27.8564i	−0.450923	+	1.68287i
$275$		0			0
$276$	2.53590	−	4.39230i	0.152643	−	0.264386i
$277$		−	16.7846i		−	1.00849i	−0.863561	−	0.504245i	$-0.831771\pi$
$277$		−	16.7846i		−	1.00849i	0.863561	−	0.504245i	$-0.168229\pi$
$278$	9.46410	+	2.53590i	0.567619	+	0.152093i
$279$		0			0
$280$		0			0
$281$	−7.92820			−0.472957			−0.236478	−	0.971637i	$-0.575993\pi$
$281$	−7.92820			−0.472957			−0.236478	+	0.971637i	$0.575993\pi$
$282$	4.09808	+	1.09808i	0.244037	+	0.0653895i
$283$			12.1244i			0.720718i	0.932814	+	0.360359i	$0.117346\pi$
$283$			12.1244i			0.720718i	−0.932814	+	0.360359i	$0.882654\pi$
$284$	7.46410	−	12.9282i	0.442913	−	0.767148i
$285$		0			0
$286$	−0.0455173	+	0.169873i	−0.00269150	+	0.0100448i
$287$	6.00000	+	6.92820i	0.354169	+	0.408959i
$288$		0			0
$289$	24.7846			1.45792
$290$		0			0
$291$			23.1962i			1.35978i
$292$	−22.3923	−	12.9282i	−1.31041	−	0.756566i
$293$	−20.3205			−1.18714			−0.593568	−	0.804784i	$-0.702281\pi$
$293$	−20.3205			−1.18714			−0.593568	+	0.804784i	$0.702281\pi$
$294$	15.7583	+	6.75833i	0.919044	+	0.394154i
$295$		0			0
$296$	18.9282	−	18.9282i	1.10018	−	1.10018i
$297$	−1.39230			−0.0807897
$298$	4.19615	+	1.12436i	0.243077	+	0.0651322i
$299$	0.679492			0.0392960
$300$		0			0
$301$	−4.00000	+	3.46410i	−0.230556	+	0.199667i
$302$	−5.56218	+	20.7583i	−0.320067	+	1.19451i
$303$	−26.7846			−1.53874
$304$	−12.0000	−	20.7846i	−0.688247	−	1.19208i
$305$		0			0
$306$		0			0
$307$		−	1.73205i		−	0.0988534i	−0.998778	−	0.0494267i	$-0.984261\pi$
$307$		−	1.73205i		−	0.0988534i	0.998778	−	0.0494267i	$-0.0157394\pi$
$308$	0.267949	+	1.39230i	0.0152678	+	0.0793339i
$309$	−11.7846			−0.670403
$310$		0			0
$311$	7.85641			0.445496			0.222748	−	0.974876i	$-0.428497\pi$
$311$	7.85641			0.445496			0.222748	+	0.974876i	$0.428497\pi$
$312$	−1.60770	+	1.60770i	−0.0910178	+	0.0910178i
$313$	17.5359			0.991188			0.495594	−	0.868554i	$-0.334950\pi$
$313$	17.5359			0.991188			0.495594	+	0.868554i	$0.334950\pi$
$314$	−10.7321	−	2.87564i	−0.605645	−	0.162282i
$315$		0			0
$316$	−14.6603	+	25.3923i	−0.824704	+	1.42843i
$317$			3.07180i			0.172529i	0.996272	+	0.0862646i	$0.0274931\pi$
$317$			3.07180i			0.172529i	−0.996272	+	0.0862646i	$0.972507\pi$
$318$	−4.73205	−	1.26795i	−0.265360	−	0.0711031i
$319$			2.12436i			0.118941i
$320$		0			0
$321$		−	4.14359i		−	0.231273i
$322$	4.92820	−	2.39230i	0.274638	−	0.133318i
$323$	38.7846			2.15803
$324$	−15.5885	−	9.00000i	−0.866025	−	0.500000i
$325$		0			0
$326$	28.3923	+	7.60770i	1.57250	+	0.421351i
$327$			3.58846i			0.198442i
$328$	−6.92820	+	6.92820i	−0.382546	+	0.382546i
$329$	3.00000	+	3.46410i	0.165395	+	0.190982i
$330$		0			0
$331$			26.3923i			1.45065i	0.688405	+	0.725326i	$0.258311\pi$
$331$			26.3923i			1.45065i	−0.688405	+	0.725326i	$0.741689\pi$
$332$	−15.4641	+	26.7846i	−0.848703	+	1.47000i
$333$		0			0
$334$	1.90192	−	7.09808i	0.104069	−	0.388389i
$335$		0			0
$336$	−6.00000	+	17.3205i	−0.327327	+	0.944911i
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	17.4641	+	4.67949i	0.949922	+	0.254531i
$339$	9.46410			0.514019
$340$		0			0
$341$			1.60770i			0.0870616i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−4.00000	−	4.00000i	−0.215666	−	0.215666i
$345$		0			0
$346$	−19.5622	−	5.24167i	−1.05167	−	0.281794i
$347$	−34.2487			−1.83857			−0.919284	−	0.393596i	$-0.871231\pi$
$347$	−34.2487			−1.83857			−0.919284	+	0.393596i	$0.871231\pi$
$348$	−13.7321	+	23.7846i	−0.736115	+	1.27499i
$349$			5.32051i			0.284800i	0.989809	+	0.142400i	$0.0454820\pi$
$349$			5.32051i			0.284800i	−0.989809	+	0.142400i	$0.954518\pi$
$350$		0			0
$351$		−	2.41154i		−	0.128719i
$352$	−1.46410	+	0.392305i	−0.0780369	+	0.0209099i
$353$	7.39230			0.393453			0.196726	−	0.980458i	$-0.436969\pi$
$353$	7.39230			0.393453			0.196726	+	0.980458i	$0.436969\pi$
$354$	−2.19615	+	8.19615i	−0.116724	+	0.435621i
$355$		0			0
$356$	2.53590	−	4.39230i	0.134402	−	0.232792i
$357$	−19.3923	−	22.3923i	−1.02635	−	1.18513i
$358$	−2.33975	+	8.73205i	−0.123659	+	0.461503i
$359$			25.3205i			1.33637i	0.743997	+	0.668183i	$0.232928\pi$
$359$			25.3205i			1.33637i	−0.743997	+	0.668183i	$0.767072\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	−0.339746	+	1.26795i	−0.0178567	+	0.0666419i
$363$		−	18.9282i		−	0.993473i
$364$	−2.41154	+	0.464102i	−0.126399	+	0.0243255i
$365$		0			0
$366$	−22.3923	−	6.00000i	−1.17046	−	0.313625i
$367$		−	11.8756i		−	0.619904i	−0.950752	−	0.309952i	$-0.899687\pi$
$367$		−	11.8756i		−	0.619904i	0.950752	−	0.309952i	$-0.100313\pi$
$368$	2.92820	+	5.07180i	0.152643	+	0.264386i
$369$		0			0
$370$		0			0
$371$	−3.46410	−	4.00000i	−0.179847	−	0.207670i
$372$	−10.3923	+	18.0000i	−0.538816	+	0.933257i
$373$		−	3.60770i		−	0.186799i	−0.995629	−	0.0933997i	$-0.970227\pi$
$373$		−	3.60770i		−	0.186799i	0.995629	−	0.0933997i	$-0.0297734\pi$
$374$	0.633975	−	2.36603i	0.0327820	−	0.122344i
$375$		0			0
$376$	−3.46410	+	3.46410i	−0.178647	+	0.178647i
$377$	−3.67949			−0.189503
$378$	−8.49038	−	17.4904i	−0.436698	−	0.899608i
$379$			5.60770i			0.288048i	0.989574	+	0.144024i	$0.0460042\pi$
$379$			5.60770i			0.288048i	−0.989574	+	0.144024i	$0.953996\pi$
$380$		0			0
$381$		−	26.7846i		−	1.37222i
$382$	−2.63397	+	9.83013i	−0.134766	+	0.502953i
$383$			27.4641i			1.40335i	0.712497	+	0.701675i	$0.247564\pi$
$383$			27.4641i			1.40335i	−0.712497	+	0.701675i	$0.752436\pi$
$384$	−18.9282	−	5.07180i	−0.965926	−	0.258819i
$385$		0			0
$386$	−3.46410	+	12.9282i	−0.176318	+	0.658028i
$387$		0			0
$388$	−23.1962	−	13.3923i	−1.17761	−	0.679891i
$389$	20.8564			1.05746			0.528731	−	0.848790i	$-0.322668\pi$
$389$	20.8564			1.05746			0.528731	+	0.848790i	$0.322668\pi$
$390$		0			0
$391$	−9.46410			−0.478620
$392$	−15.8564	+	11.8564i	−0.800869	+	0.598839i
$393$		−	4.39230i		−	0.221562i
$394$	4.87564	−	18.1962i	0.245631	−	0.916709i
$395$		0			0
$396$		0			0
$397$	12.4641			0.625555			0.312778	−	0.949826i	$-0.398741\pi$
$397$	12.4641			0.625555			0.312778	+	0.949826i	$0.398741\pi$
$398$	4.73205	+	1.26795i	0.237196	+	0.0635566i
$399$	−18.0000	−	20.7846i	−0.901127	−	1.04053i
$400$		0			0
$401$	−10.0718			−0.502962			−0.251481	−	0.967862i	$-0.580918\pi$
$401$	−10.0718			−0.502962			−0.251481	+	0.967862i	$0.580918\pi$
$402$	−2.19615	+	8.19615i	−0.109534	+	0.408787i
$403$	−2.78461			−0.138711
$404$	15.4641	−	26.7846i	0.769368	−	1.33258i
$405$		0			0
$406$	−26.6865	+	12.9545i	−1.32443	+	0.642920i
$407$	2.53590			0.125700
$408$	22.3923	−	22.3923i	1.10858	−	1.10858i
$409$		−	4.14359i		−	0.204888i	−0.994739	−	0.102444i	$-0.967334\pi$
$409$		−	4.14359i		−	0.204888i	0.994739	−	0.102444i	$-0.0326662\pi$
$410$		0			0
$411$	−35.3205			−1.74223
$412$	6.80385	−	11.7846i	0.335202	−	0.580586i
$413$	−6.92820	+	6.00000i	−0.340915	+	0.295241i
$414$		0			0
$415$		0			0
$416$	−0.679492	−	2.53590i	−0.0333148	−	0.124333i
$417$			12.0000i			0.587643i
$418$	0.588457	−	2.19615i	0.0287824	−	0.107417i
$419$	24.2487			1.18463			0.592314	−	0.805708i	$-0.298215\pi$
$419$	24.2487			1.18463			0.592314	+	0.805708i	$0.298215\pi$
$420$		0			0
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	−1.16987	+	4.36603i	−0.0569485	+	0.212535i
$423$		0			0
$424$	4.00000	−	4.00000i	0.194257	−	0.194257i
$425$		0			0
$426$	17.6603	+	4.73205i	0.855642	+	0.229269i
$427$	−16.3923	−	18.9282i	−0.793279	−	0.916000i
$428$	4.14359	+	2.39230i	0.200288	+	0.115636i
$429$	−0.215390			−0.0103991
$430$		0			0
$431$			13.5885i			0.654533i	0.944932	+	0.327266i	$0.106127\pi$
$431$			13.5885i			0.654533i	−0.944932	+	0.327266i	$0.893873\pi$
$432$	18.0000	−	10.3923i	0.866025	−	0.500000i
$433$	31.8564			1.53092			0.765461	−	0.643483i	$-0.222511\pi$
$433$	31.8564			1.53092			0.765461	+	0.643483i	$0.222511\pi$
$434$	−20.1962	+	9.80385i	−0.969446	+	0.470600i
$435$		0			0
$436$	−3.58846	−	2.07180i	−0.171856	−	0.0992211i
$437$	−8.78461			−0.420225
$438$	8.19615	−	30.5885i	0.391627	−	1.46157i
$439$	39.7128			1.89539			0.947695	−	0.319179i	$-0.103407\pi$
$439$	39.7128			1.89539			0.947695	+	0.319179i	$0.103407\pi$
$440$		0			0
$441$		0			0
$442$	4.09808	+	1.09808i	0.194926	+	0.0522302i
$443$	−26.0000			−1.23530			−0.617649	−	0.786454i	$-0.711915\pi$
$443$	−26.0000			−1.23530			−0.617649	+	0.786454i	$0.711915\pi$
$444$	28.3923	+	16.3923i	1.34744	+	0.777944i
$445$		0			0
$446$	−5.02628	+	18.7583i	−0.238001	+	0.888233i
$447$			5.32051i			0.251651i
$448$	−13.8564	−	16.0000i	−0.654654	−	0.755929i
$449$	−11.9282			−0.562927			−0.281463	−	0.959572i	$-0.590820\pi$
$449$	−11.9282			−0.562927			−0.281463	+	0.959572i	$0.590820\pi$
$450$		0			0
$451$	−0.928203			−0.0437074
$452$	−5.46410	+	9.46410i	−0.257010	+	0.445154i
$453$	−26.3205			−1.23665
$454$	−7.56218	+	28.2224i	−0.354911	+	1.32454i
$455$		0			0
$456$	20.7846	−	20.7846i	0.973329	−	0.973329i
$457$		−	20.5359i		−	0.960629i	−0.877096	−	0.480314i	$-0.840523\pi$
$457$		−	20.5359i		−	0.960629i	0.877096	−	0.480314i	$-0.159477\pi$
$458$	3.12436	−	11.6603i	0.145992	−	0.544848i
$459$			33.5885i			1.56777i
$460$		0			0
$461$			27.7128i			1.29071i	0.763881	+	0.645357i	$0.223291\pi$
$461$			27.7128i			1.29071i	−0.763881	+	0.645357i	$0.776709\pi$
$462$	−1.56218	+	0.758330i	−0.0726791	+	0.0352807i
$463$	−16.3923			−0.761815			−0.380908	−	0.924613i	$-0.624388\pi$
$463$	−16.3923			−0.761815			−0.380908	+	0.924613i	$0.624388\pi$
$464$	−15.8564	−	27.4641i	−0.736115	−	1.27499i
$465$		0			0
$466$	−3.32051	+	12.3923i	−0.153820	+	0.574062i
$467$		−	22.5167i		−	1.04195i	−0.853573	−	0.520973i	$-0.825569\pi$
$467$		−	22.5167i		−	1.04195i	0.853573	−	0.520973i	$-0.174431\pi$
$468$		0			0
$469$	−6.92820	+	6.00000i	−0.319915	+	0.277054i
$470$		0			0
$471$		−	13.6077i		−	0.627009i
$472$	−6.92820	−	6.92820i	−0.318896	−	0.318896i
$473$		−	0.535898i		−	0.0246406i
$474$	−34.6865	−	9.29423i	−1.59321	−	0.426898i
$475$		0			0
$476$	33.5885	−	6.46410i	1.53952	−	0.296282i
$477$		0			0
$478$	−8.77757	+	32.7583i	−0.401477	+	1.49833i
$479$	−25.1769			−1.15036			−0.575181	−	0.818026i	$-0.695068\pi$
$479$	−25.1769			−1.15036			−0.575181	+	0.818026i	$0.695068\pi$
$480$		0			0
$481$			4.39230i			0.200272i
$482$	6.00000	−	22.3923i	0.273293	−	1.01994i
$483$	4.39230	+	5.07180i	0.199857	+	0.230775i
$484$	18.9282	+	10.9282i	0.860373	+	0.496737i
$485$		0			0
$486$		0			0
$487$	12.7846			0.579326			0.289663	−	0.957129i	$-0.406457\pi$
$487$	12.7846			0.579326			0.289663	+	0.957129i	$0.406457\pi$
$488$	18.9282	−	18.9282i	0.856840	−	0.856840i
$489$			36.0000i			1.62798i
$490$		0			0
$491$			9.87564i			0.445682i	0.974855	+	0.222841i	$0.0715330\pi$
$491$			9.87564i			0.445682i	−0.974855	+	0.222841i	$0.928467\pi$
$492$	−10.3923	−	6.00000i	−0.468521	−	0.270501i
$493$	51.2487			2.30813
$494$	3.80385	+	1.01924i	0.171143	+	0.0458577i
$495$		0			0
$496$	−12.0000	−	20.7846i	−0.538816	−	0.933257i
$497$	12.9282	+	14.9282i	0.579909	+	0.669621i
$498$	−36.5885	−	9.80385i	−1.63957	−	0.439321i
$499$			25.5885i			1.14550i	0.819731	+	0.572748i	$0.194123\pi$
$499$			25.5885i			1.14550i	−0.819731	+	0.572748i	$0.805877\pi$
$500$		0			0
$501$	9.00000			0.402090
$502$	35.3205	+	9.46410i	1.57643	+	0.422404i
$503$		−	15.5885i		−	0.695055i	−0.937670	−	0.347527i	$-0.887021\pi$
$503$		−	15.5885i		−	0.695055i	0.937670	−	0.347527i	$-0.112979\pi$
$504$		0			0
$505$		0			0
$506$	−0.143594	+	0.535898i	−0.00638351	+	0.0238236i
$507$			22.1436i			0.983432i
$508$	26.7846	+	15.4641i	1.18837	+	0.686109i
$509$		−	25.8564i		−	1.14607i	−0.819533	−	0.573033i	$-0.805767\pi$
$509$		−	25.8564i		−	1.14607i	0.819533	−	0.573033i	$-0.194233\pi$
$510$		0			0
$511$	25.8564	−	22.3923i	1.14382	−	0.990577i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$			31.1769i			1.37649i
$514$	−8.19615	−	2.19615i	−0.361517	−	0.0968681i
$515$		0			0
$516$	3.46410	−	6.00000i	0.152499	−	0.264135i
$517$	−0.464102			−0.0204112
$518$	15.4641	+	31.8564i	0.679454	+	1.39969i
$519$		−	24.8038i		−	1.08877i
$520$		0			0
$521$			13.6077i			0.596164i	0.954540	+	0.298082i	$0.0963469\pi$
$521$			13.6077i			0.596164i	−0.954540	+	0.298082i	$0.903653\pi$
$522$		0			0
$523$		−	24.2487i		−	1.06032i	−0.847897	−	0.530161i	$-0.822131\pi$
$523$		−	24.2487i		−	1.06032i	0.847897	−	0.530161i	$-0.177869\pi$
$524$	4.39230	+	2.53590i	0.191879	+	0.110781i
$525$		0			0
$526$	15.6603	+	4.19615i	0.682820	+	0.182961i
$527$	38.7846			1.68948
$528$	−0.928203	−	1.60770i	−0.0403949	−	0.0699660i
$529$	−20.8564			−0.906800
$530$		0			0
$531$		0			0
$532$	31.1769	−	6.00000i	1.35169	−	0.260133i
$533$		−	1.60770i		−	0.0696370i
$534$	6.00000	+	1.60770i	0.259645	+	0.0695718i
$535$		0			0
$536$	−6.92820	−	6.92820i	−0.299253	−	0.299253i
$537$	−11.0718			−0.477783
$538$	4.39230	−	16.3923i	0.189366	−	0.706722i
$539$	−1.85641	−	0.267949i	−0.0799611	−	0.0115414i
$540$		0			0
$541$	7.78461			0.334687			0.167343	−	0.985899i	$-0.446481\pi$
$541$	7.78461			0.334687			0.167343	+	0.985899i	$0.446481\pi$
$542$	−12.9282	−	3.46410i	−0.555314	−	0.148796i
$543$	−1.60770			−0.0689928
$544$	9.46410	+	35.3205i	0.405770	+	1.51435i
$545$		0			0
$546$	−1.31347	−	2.70577i	−0.0562112	−	0.115796i
$547$	−21.4641			−0.917739			−0.458869	−	0.888504i	$-0.651745\pi$
$547$	−21.4641			−0.917739			−0.458869	+	0.888504i	$0.651745\pi$
$548$	20.3923	−	35.3205i	0.871116	−	1.50882i
$549$		0			0
$550$		0			0
$551$	47.5692			2.02652
$552$	−5.07180	+	5.07180i	−0.215870	+	0.215870i
$553$	−25.3923	−	29.3205i	−1.07979	−	1.24683i
$554$	−6.14359	+	22.9282i	−0.261016	+	0.974126i
$555$		0			0
$556$	−12.0000	−	6.92820i	−0.508913	−	0.293821i
$557$			21.8564i			0.926086i	0.886336	+	0.463043i	$0.153242\pi$
$557$			21.8564i			0.926086i	−0.886336	+	0.463043i	$0.846758\pi$
$558$		0			0
$559$	0.928203			0.0392588
$560$		0			0
$561$	3.00000			0.126660
$562$	10.8301	+	2.90192i	0.456841	+	0.122410i
$563$			19.1769i			0.808211i	0.914712	+	0.404105i	$0.132417\pi$
$563$			19.1769i			0.808211i	−0.914712	+	0.404105i	$0.867583\pi$
$564$	−5.19615	−	3.00000i	−0.218797	−	0.126323i
$565$		0			0
$566$	4.43782	−	16.5622i	0.186536	−	0.696160i
$567$	18.0000	−	15.5885i	0.755929	−	0.654654i
$568$	−14.9282	+	14.9282i	−0.626373	+	0.626373i
$569$	−7.07180			−0.296465			−0.148233	−	0.988953i	$-0.547358\pi$
$569$	−7.07180			−0.296465			−0.148233	+	0.988953i	$0.547358\pi$
$570$		0			0
$571$			6.67949i			0.279528i	0.990185	+	0.139764i	$0.0446344\pi$
$571$			6.67949i			0.279528i	−0.990185	+	0.139764i	$0.955366\pi$
$572$	0.124356	−	0.215390i	0.00519957	−	0.00900592i
$573$	−12.4641			−0.520695
$574$	−5.66025	−	11.6603i	−0.236254	−	0.486690i
$575$		0			0
$576$		0			0
$577$	19.3923			0.807312			0.403656	−	0.914911i	$-0.367739\pi$
$577$	19.3923			0.807312			0.403656	+	0.914911i	$0.367739\pi$
$578$	−33.8564	−	9.07180i	−1.40824	−	0.377337i
$579$	−16.3923			−0.681241
$580$		0			0
$581$	−26.7846	−	30.9282i	−1.11121	−	1.28312i
$582$	8.49038	−	31.6865i	0.351938	−	1.31345i
$583$	0.535898			0.0221946
$584$	25.8564	+	25.8564i	1.06995	+	1.06995i
$585$		0			0
$586$	27.7583	+	7.43782i	1.14669	+	0.307254i
$587$			20.5359i			0.847607i	0.905754	+	0.423804i	$0.139305\pi$
$587$			20.5359i			0.847607i	−0.905754	+	0.423804i	$0.860695\pi$
$588$	−19.0526	−	15.0000i	−0.785714	−	0.618590i
$589$	36.0000			1.48335
$590$		0			0
$591$	23.0718			0.949047
$592$	−32.7846	+	18.9282i	−1.34744	+	0.777944i
$593$	−30.4641			−1.25101			−0.625505	−	0.780220i	$-0.715107\pi$
$593$	−30.4641			−1.25101			−0.625505	+	0.780220i	$0.715107\pi$
$594$	1.90192	+	0.509619i	0.0780369	+	0.0209099i
$595$		0			0
$596$	−5.32051	−	3.07180i	−0.217937	−	0.125826i
$597$			6.00000i			0.245564i
$598$	−0.928203	−	0.248711i	−0.0379571	−	0.0101706i
$599$		−	10.1244i		−	0.413670i	−0.978376	−	0.206835i	$-0.933684\pi$
$599$		−	10.1244i		−	0.413670i	0.978376	−	0.206835i	$-0.0663163\pi$
$600$		0			0
$601$		−	14.7846i		−	0.603077i	−0.953454	−	0.301538i	$-0.902500\pi$
$601$		−	14.7846i		−	0.603077i	0.953454	−	0.301538i	$-0.0975001\pi$
$602$	6.73205	−	3.26795i	0.274378	−	0.133192i
$603$		0			0
$604$	15.1962	−	26.3205i	0.618323	−	1.07097i
$605$		0			0
$606$	36.5885	+	9.80385i	1.48630	+	0.398254i
$607$			29.1962i			1.18504i	0.805557	+	0.592518i	$0.201866\pi$
$607$			29.1962i			1.18504i	−0.805557	+	0.592518i	$0.798134\pi$
$608$	8.78461	+	32.7846i	0.356263	+	1.32959i
$609$	−23.7846	−	27.4641i	−0.963801	−	1.11290i
$610$		0			0
$611$		−	0.803848i		−	0.0325202i
$612$		0			0
$613$		−	10.0000i		−	0.403896i	−0.979396	−	0.201948i	$-0.935273\pi$
$613$		−	10.0000i		−	0.403896i	0.979396	−	0.201948i	$-0.0647272\pi$
$614$	−0.633975	+	2.36603i	−0.0255851	+	0.0954850i
$615$		0			0
$616$	0.143594	−	2.00000i	0.00578555	−	0.0805823i
$617$			22.9282i			0.923055i	0.887126	+	0.461527i	$0.152698\pi$
$617$			22.9282i			0.923055i	−0.887126	+	0.461527i	$0.847302\pi$
$618$	16.0981	+	4.31347i	0.647560	+	0.173513i
$619$	−0.679492			−0.0273111			−0.0136555	−	0.999907i	$-0.504347\pi$
$619$	−0.679492			−0.0273111			−0.0136555	+	0.999907i	$0.504347\pi$
$620$		0			0
$621$		−	7.60770i		−	0.305286i
$622$	−10.7321	−	2.87564i	−0.430316	−	0.115303i
$623$	4.39230	+	5.07180i	0.175974	+	0.203197i
$624$	2.78461	−	1.60770i	0.111474	−	0.0643593i
$625$		0			0
$626$	−23.9545	−	6.41858i	−0.957414	−	0.256538i
$627$	2.78461			0.111207
$628$	13.6077	+	7.85641i	0.543006	+	0.313505i
$629$		−	61.1769i		−	2.43928i
$630$		0			0
$631$		−	38.9090i		−	1.54894i	−0.632610	−	0.774471i	$-0.718016\pi$
$631$		−	38.9090i		−	1.54894i	0.632610	−	0.774471i	$-0.281984\pi$
$632$	29.3205	−	29.3205i	1.16631	−	1.16631i
$633$	−5.53590			−0.220032
$634$	1.12436	−	4.19615i	0.0446539	−	0.166651i
$635$		0			0
$636$	6.00000	+	3.46410i	0.237915	+	0.137361i
$637$	0.464102	−	3.21539i	0.0183884	−	0.127398i
$638$	0.777568	−	2.90192i	0.0307842	−	0.114888i
$639$		0			0
$640$		0			0
$641$	8.92820			0.352643			0.176321	−	0.984333i	$-0.443580\pi$
$641$	8.92820			0.352643			0.176321	+	0.984333i	$0.443580\pi$
$642$	−1.51666	+	5.66025i	−0.0598578	+	0.223392i
$643$			7.05256i			0.278126i	0.990284	+	0.139063i	$0.0444090\pi$
$643$			7.05256i			0.278126i	−0.990284	+	0.139063i	$0.955591\pi$
$644$	−7.60770	+	1.46410i	−0.299785	+	0.0576937i
$645$		0			0
$646$	−52.9808	−	14.1962i	−2.08450	−	0.558540i
$647$			10.3923i			0.408564i	0.978912	+	0.204282i	$0.0654859\pi$
$647$			10.3923i			0.408564i	−0.978912	+	0.204282i	$0.934514\pi$
$648$	18.0000	+	18.0000i	0.707107	+	0.707107i
$649$		−	0.928203i		−	0.0364352i
$650$		0			0
$651$	−18.0000	−	20.7846i	−0.705476	−	0.814613i
$652$	−36.0000	−	20.7846i	−1.40987	−	0.813988i
$653$			17.6077i			0.689042i	0.938779	+	0.344521i	$0.111959\pi$
$653$			17.6077i			0.689042i	−0.938779	+	0.344521i	$0.888041\pi$
$654$	1.31347	−	4.90192i	0.0513606	−	0.191680i
$655$		0			0
$656$	12.0000	−	6.92820i	0.468521	−	0.270501i
$657$		0			0
$658$	−2.83013	−	5.83013i	−0.110330	−	0.227282i
$659$		−	31.1962i		−	1.21523i	−0.794232	−	0.607615i	$-0.792126\pi$
$659$		−	31.1962i		−	1.21523i	0.794232	−	0.607615i	$-0.207874\pi$
$660$		0			0
$661$			39.7128i			1.54465i	0.635228	+	0.772325i	$0.280906\pi$
$661$			39.7128i			1.54465i	−0.635228	+	0.772325i	$0.719094\pi$
$662$	9.66025	−	36.0526i	0.375456	−	1.40122i
$663$			5.19615i			0.201802i
$664$	30.9282	−	30.9282i	1.20025	−	1.20025i
$665$		0			0
$666$		0			0
$667$	−11.6077			−0.449452
$668$	−5.19615	+	9.00000i	−0.201045	+	0.348220i
$669$	−23.7846			−0.919566
$670$		0			0
$671$	2.53590			0.0978973
$672$	14.5359	−	21.4641i	0.560734	−	0.827996i
$673$		−	13.1769i		−	0.507933i	−0.967213	−	0.253966i	$-0.918265\pi$
$673$		−	13.1769i		−	0.507933i	0.967213	−	0.253966i	$-0.0817353\pi$
$674$		0			0
$675$		0			0
$676$	−22.1436	−	12.7846i	−0.851677	−	0.491716i
$677$	−25.3923			−0.975906			−0.487953	−	0.872870i	$-0.662256\pi$
$677$	−25.3923			−0.975906			−0.487953	+	0.872870i	$0.662256\pi$
$678$	−12.9282	−	3.46410i	−0.496505	−	0.133038i
$679$	26.7846	−	23.1962i	1.02790	−	0.890187i
$680$		0			0
$681$	−35.7846			−1.37127
$682$	0.588457	−	2.19615i	0.0225332	−	0.0840950i
$683$	7.32051			0.280111			0.140056	−	0.990144i	$-0.455272\pi$
$683$	7.32051			0.280111			0.140056	+	0.990144i	$0.455272\pi$
$684$		0			0
$685$		0			0
$686$	−7.95448	−	24.9545i	−0.303704	−	0.952767i
$687$	14.7846			0.564068
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$			0.928203i			0.0353617i
$690$		0			0
$691$	−22.6410			−0.861305			−0.430652	−	0.902518i	$-0.641717\pi$
$691$	−22.6410			−0.861305			−0.430652	+	0.902518i	$0.641717\pi$
$692$	24.8038	+	14.3205i	0.942901	+	0.544384i
$693$		0			0
$694$	46.7846	+	12.5359i	1.77592	+	0.475856i
$695$		0			0
$696$	27.4641	−	27.4641i	1.04102	−	1.04102i
$697$			22.3923i			0.848169i
$698$	1.94744	−	7.26795i	0.0737117	−	0.275096i
$699$	−15.7128			−0.594313
$700$		0			0
$701$	−37.7846			−1.42711			−0.713553	−	0.700602i	$-0.752915\pi$
$701$	−37.7846			−1.42711			−0.713553	+	0.700602i	$0.752915\pi$
$702$	−0.882686	+	3.29423i	−0.0333148	+	0.124333i
$703$		−	56.7846i		−	2.14167i
$704$	2.14359			0.0807897
$705$		0			0
$706$	−10.0981	−	2.70577i	−0.380046	−	0.101833i
$707$	26.7846	+	30.9282i	1.00734	+	1.16317i
$708$	6.00000	−	10.3923i	0.225494	−	0.390567i
$709$	−21.0000			−0.788672			−0.394336	−	0.918966i	$-0.629025\pi$
$709$	−21.0000			−0.788672			−0.394336	+	0.918966i	$0.629025\pi$
$710$		0			0
$711$		0			0
$712$	−5.07180	+	5.07180i	−0.190074	+	0.190074i
$713$	−8.78461			−0.328986
$714$	18.2942	+	37.6865i	0.684644	+	1.41038i
$715$		0			0
$716$	6.39230	−	11.0718i	0.238892	−	0.413772i
$717$	−41.5359			−1.55119
$718$	9.26795	−	34.5885i	0.345877	−	1.29083i
$719$	−38.5359			−1.43715			−0.718573	−	0.695451i	$-0.755205\pi$
$719$	−38.5359			−1.43715			−0.718573	+	0.695451i	$0.755205\pi$
$720$		0			0
$721$	11.7846	+	13.6077i	0.438882	+	0.506777i
$722$	−23.2224	−	6.22243i	−0.864249	−	0.231575i
$723$	28.3923			1.05592
$724$	0.928203	−	1.60770i	0.0344964	−	0.0597495i
$725$		0			0
$726$	−6.92820	+	25.8564i	−0.257130	+	0.959621i
$727$			13.6077i			0.504681i	0.967638	+	0.252341i	$0.0812004\pi$
$727$			13.6077i			0.504681i	−0.967638	+	0.252341i	$0.918800\pi$
$728$	3.46410	+	0.248711i	0.128388	+	0.00921785i
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−12.9282			−0.478167
$732$	28.3923	+	16.3923i	1.04941	+	0.605877i
$733$	−11.5359			−0.426088			−0.213044	−	0.977043i	$-0.568338\pi$
$733$	−11.5359			−0.426088			−0.213044	+	0.977043i	$0.568338\pi$
$734$	−4.34679	+	16.2224i	−0.160443	+	0.598781i
$735$		0			0
$736$	−2.14359	−	8.00000i	−0.0790139	−	0.294884i
$737$		−	0.928203i		−	0.0341908i
$738$		0			0
$739$		−	4.26795i		−	0.156999i	−0.996914	−	0.0784995i	$-0.974987\pi$
$739$		−	4.26795i		−	0.156999i	0.996914	−	0.0784995i	$-0.0250129\pi$
$740$		0			0
$741$			4.82309i			0.177180i
$742$	3.26795	+	6.73205i	0.119970	+	0.247141i
$743$	30.3923			1.11499			0.557493	−	0.830182i	$-0.311763\pi$
$743$	30.3923			1.11499			0.557493	+	0.830182i	$0.311763\pi$
$744$	20.7846	−	20.7846i	0.762001	−	0.762001i
$745$		0			0
$746$	−1.32051	+	4.92820i	−0.0483472	+	0.180434i
$747$		0			0
$748$	−1.73205	+	3.00000i	−0.0633300	+	0.109691i
$749$	−4.78461	+	4.14359i	−0.174826	+	0.151404i
$750$		0			0
$751$			25.5885i			0.933736i	0.884327	+	0.466868i	$0.154618\pi$
$751$			25.5885i			0.933736i	−0.884327	+	0.466868i	$0.845382\pi$
$752$	6.00000	−	3.46410i	0.218797	−	0.126323i
$753$			44.7846i			1.63204i
$754$	5.02628	+	1.34679i	0.183046	+	0.0490471i
$755$		0			0
$756$	5.19615	+	27.0000i	0.188982	+	0.981981i
$757$		−	37.8564i		−	1.37591i	−0.725751	−	0.687957i	$-0.758508\pi$
$757$		−	37.8564i		−	1.37591i	0.725751	−	0.687957i	$-0.241492\pi$
$758$	2.05256	−	7.66025i	0.0745523	−	0.278233i
$759$	−0.679492			−0.0246640
$760$		0			0
$761$		−	42.2487i		−	1.53151i	−0.643130	−	0.765757i	$-0.722364\pi$
$761$		−	42.2487i		−	1.53151i	0.643130	−	0.765757i	$-0.277636\pi$
$762$	−9.80385	+	36.5885i	−0.355156	+	1.32546i
$763$	4.14359	−	3.58846i	0.150008	−	0.129911i
$764$	7.19615	−	12.4641i	0.260348	−	0.450935i
$765$		0			0
$766$	10.0526	−	37.5167i	0.363214	−	1.35553i
$767$	1.60770			0.0580505
$768$	24.0000	+	13.8564i	0.866025	+	0.500000i
$769$		−	18.0000i		−	0.649097i	−0.945869	−	0.324548i	$-0.894788\pi$
$769$		−	18.0000i		−	0.649097i	0.945869	−	0.324548i	$-0.105212\pi$
$770$		0			0
$771$		−	10.3923i		−	0.374270i
$772$	9.46410	−	16.3923i	0.340620	−	0.589972i
$773$	5.53590			0.199112			0.0995562	−	0.995032i	$-0.468258\pi$
$773$	5.53590			0.199112			0.0995562	+	0.995032i	$0.468258\pi$
$774$		0			0
$775$		0			0
$776$	26.7846	+	26.7846i	0.961511	+	0.961511i
$777$	−32.7846	+	28.3923i	−1.17614	+	1.01857i
$778$	−28.4904	−	7.63397i	−1.02143	−	0.273691i
$779$			20.7846i			0.744686i
$780$		0			0
$781$	−2.00000			−0.0715656

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 + 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.36603 - 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 + 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} -0.267949i q^{11} +(1.73205 - 3.00000i) q^{12} +0.464102 q^{13} +(3.36603 - 1.63397i) q^{14} +(2.00000 + 3.46410i) q^{16} -6.46410 q^{17} -6.00000 q^{19} +(3.00000 + 3.46410i) q^{21} +(-0.0980762 + 0.366025i) q^{22} +1.46410 q^{23} +(-3.46410 + 3.46410i) q^{24} +(-0.633975 - 0.169873i) q^{26} -5.19615i q^{27} +(-5.19615 + 1.00000i) q^{28} -7.92820 q^{29} -6.00000 q^{31} +(-1.46410 - 5.46410i) q^{32} -0.464102 q^{33} +(8.83013 + 2.36603i) q^{34} +9.46410i q^{37} +(8.19615 + 2.19615i) q^{38} -0.803848i q^{39} -3.46410i q^{41} +(-2.83013 - 5.83013i) q^{42} +2.00000 q^{43} +(0.267949 - 0.464102i) q^{44} +(-2.00000 - 0.535898i) q^{46} -1.73205i q^{47} +(6.00000 - 3.46410i) q^{48} +(1.00000 - 6.92820i) q^{49} +11.1962i q^{51} +(0.803848 + 0.464102i) q^{52} +2.00000i q^{53} +(-1.90192 + 7.09808i) q^{54} +(7.46410 + 0.535898i) q^{56} +10.3923i q^{57} +(10.8301 + 2.90192i) q^{58} +3.46410 q^{59} +9.46410i q^{61} +(8.19615 + 2.19615i) q^{62} +8.00000i q^{64} +(0.633975 + 0.169873i) q^{66} +3.46410 q^{67} +(-11.1962 - 6.46410i) q^{68} -2.53590i q^{69} -7.46410i q^{71} -12.9282 q^{73} +(3.46410 - 12.9282i) q^{74} +(-10.3923 - 6.00000i) q^{76} +(0.464102 + 0.535898i) q^{77} +(-0.294229 + 1.09808i) q^{78} +14.6603i q^{79} -9.00000 q^{81} +(-1.26795 + 4.73205i) q^{82} +15.4641i q^{83} +(1.73205 + 9.00000i) q^{84} +(-2.73205 - 0.732051i) q^{86} +13.7321i q^{87} +(-0.535898 + 0.535898i) q^{88} -2.53590i q^{89} +(-0.928203 + 0.803848i) q^{91} +(2.53590 + 1.46410i) q^{92} +10.3923i q^{93} +(-0.633975 + 2.36603i) q^{94} +(-9.46410 + 2.53590i) q^{96} -13.3923 q^{97} +(-3.90192 + 9.09808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{6} - 8 q^{7} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^6 - 8 * q^7 - 8 * q^8	\( 4 q - 2 q^{2} - 6 q^{6} - 8 q^{7} - 8 q^{8} - 12 q^{13} + 10 q^{14} + 8 q^{16} - 12 q^{17} - 24 q^{19} + 12 q^{21} + 10 q^{22} - 8 q^{23} - 6 q^{26} - 4 q^{29} - 24 q^{31} + 8 q^{32} + 12 q^{33} + 18 q^{34} + 12 q^{38} + 6 q^{42} + 8 q^{43} + 8 q^{44} - 8 q^{46} + 24 q^{48} + 4 q^{49} + 24 q^{52} - 18 q^{54} + 16 q^{56} + 26 q^{58} + 12 q^{62} + 6 q^{66} - 24 q^{68} - 24 q^{73} - 12 q^{77} + 30 q^{78} - 36 q^{81} - 12 q^{82} - 4 q^{86} - 16 q^{88} + 24 q^{91} + 24 q^{92} - 6 q^{94} - 24 q^{96} - 12 q^{97} - 26 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^6 - 8 * q^7 - 8 * q^8 - 12 * q^13 + 10 * q^14 + 8 * q^16 - 12 * q^17 - 24 * q^19 + 12 * q^21 + 10 * q^22 - 8 * q^23 - 6 * q^26 - 4 * q^29 - 24 * q^31 + 8 * q^32 + 12 * q^33 + 18 * q^34 + 12 * q^38 + 6 * q^42 + 8 * q^43 + 8 * q^44 - 8 * q^46 + 24 * q^48 + 4 * q^49 + 24 * q^52 - 18 * q^54 + 16 * q^56 + 26 * q^58 + 12 * q^62 + 6 * q^66 - 24 * q^68 - 24 * q^73 - 12 * q^77 + 30 * q^78 - 36 * q^81 - 12 * q^82 - 4 * q^86 - 16 * q^88 + 24 * q^91 + 24 * q^92 - 6 * q^94 - 24 * q^96 - 12 * q^97 - 26 * q^98

Introduction

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